We study in a systematic way $ZH$ production in the Standard Model Effective Field Theory framework. We first calculate analytical expressions for the helicity amplitudes of the gluon-induced channel with up to one insertion of a CP-even dimension-6 operator. We then study the high-energy behaviour of the helicity amplitudes in order to identify to which operators $gg \rightarrow ZH$ is most sensitive. Additionally, we conduct a phenomenological analysis of $ZH$ production, considering both quark and gluon initial states. We find that for some third-generation operators, the loop-induced channel provides competitive sensitivity to constraints obtained from top quark production processes. Finally we consider CP-odd operators and extend the SMEFTatNLO implementation to include the CP-violating top Yukawa operator, and present preliminary results of its impact on gluon-induced $ZH$ production.